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Nonlinear Evolution Equation and Applications

Nonlinear evolution equations are mathematical models rich in structure and leading to many applications.

The members of the group in particular study:

 

  • p-laplacian and curvature flow in groups, with a subriemannian metric. In this setting Lie derivatives take the place of  partial derivatives and the characteristic form of parabolic equation in this setting has smallest eigenvalue identically zero.  Existence, regularity Schauder estimates at the boundary and asymptotic behavior are still open in this setting
  • nonlinear waves associated to integrable Hamiltonian models (KdV and KP hierarchies) and their finite dimensional reductions.
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    Applications of the research include:

     

  • soap films and minimal surfaces
  • models of vision and eyes path tracking
  • image analysis
  • rogue waves analysis
  • shallow water waves
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    Members of the Group:

    Simonetta Abenda

    Giovanna Citti

    Collaborations:

    A. Sarti (EHESS CAMS Paris),

    L. Capogna (Worcester Polytechnic Institute),

    S. Zucker (Yale University),

    Petr G. Grinevich (Moscow University and Landau Institue of Theoretical Physics),

    Tamara Grava (SISSA and University of Bristol).